## Description

https://leetcode.com/problems/maximum-frequency-stack/

Implement `FreqStack`

, a class which simulates the operation of a stack-like data structure.

`FreqStack`

has two functions:

`push(int x)`

, which pushes an integer`x`

onto the stack.`pop()`

, which**removes**and returns the most frequent element in the stack.- If there is a tie for most frequent element, the element closest to the top of the stack is removed and returned.

**Example 1:**

Input:["FreqStack","push","push","push","push","push","push","pop","pop","pop","pop"], [[],[5],[7],[5],[7],[4],[5],[],[],[],[]]Output:[null,null,null,null,null,null,null,5,7,5,4]Explanation: After making six .push operations, the stack is [5,7,5,7,4,5] from bottom to top. Then: pop() -> returns 5, as 5 is the most frequent. The stack becomes [5,7,5,7,4]. pop() -> returns 7, as 5 and 7 is the most frequent, but 7 is closest to the top. The stack becomes [5,7,5,4]. pop() -> returns 5. The stack becomes [5,7,4]. pop() -> returns 4. The stack becomes [5,7].

**Note:**

- Calls to
`FreqStack.push(int x)`

will be such that`0 <= x <= 10^9`

. - It is guaranteed that
`FreqStack.pop()`

won’t be called if the stack has zero elements. - The total number of
`FreqStack.push`

calls will not exceed`10000`

in a single test case. - The total number of
`FreqStack.pop`

calls will not exceed`10000`

in a single test case. - The total number of
`FreqStack.push`

and`FreqStack.pop`

calls will not exceed`150000`

across all test cases.

## Explanation

keep track of the frequency, max frequency, and what are the elements of each frequency

## Python Solution

```
class FreqStack:
def __init__(self):
self.frequency = collections.Counter()
self.frequency_groups = collections.defaultdict(list)
self.max_frequency = 0
def push(self, x: int) -> None:
frequency = self.frequency[x] + 1
self.frequency[x] = frequency
if frequency > self.max_frequency:
self.max_frequency = frequency
self.frequency_groups[frequency].append(x)
def pop(self) -> int:
value = self.frequency_groups[self.max_frequency].pop()
self.frequency[value] -= 1
if not self.frequency_groups[self.max_frequency]:
self.max_frequency -= 1
return value
# Your FreqStack object will be instantiated and called as such:
# obj = FreqStack()
# obj.push(x)
# param_2 = obj.pop()
```

- Time Complexity: ~1
- Space Complexity: ~N